Inequality Sum
posted by HELP ME...uRGENT! on .
x,y and z are positive integers such that x<y,x+y=201,z−x=200. What is the maximum value of x+y+z?

x + y = 201
y = 201  x
y > x that's why x < 201 / 2
x < 100.5
Nearest integer:
x = 100
x + y = 201
y = 201  x
y = 201  100
y = 101
z − x = 200
z = 200 + x
z = 200 + 100
z = 300
x + y + z = 100 + 101 + 300 = 501 
OR
x + y = 201
y = 201  x
z − x = 200
z = 200 + x
x + y + z = x + 201  x + 200 + x
x + y + z = 401 + x
x + y = 201
mean :
x < 201 / 2
x < 100.5
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For example :
If x = 101
y = 201  x = 201  101 = 100
That not satisfie condition :
x < y
If x = 102
y = 201  x = 201  102 = 99
That not satisfie condition :
x < y
If x = 103
y = 201  x = 201  103 = 98
That not satisfie condition :
x < y
etc.
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That's why :
x < 201 / 2
x < 100.5
Largest integer less of 100.5 are 100
so
x = 100
x + y + z = 401 + x = 401 + 100 = 501